1 citations · 2 across the 5 of their papers we have counts for
5 papers
Kinetic-based regularization: Learning spatial derivatives and PDE applications
Abhisek Ganguly, Santosh Ansumali, Sauro Succi
Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regulariz…
Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Abhisek Ganguly, Santosh Ansumali, Sauro Succi
We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differ…
Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems
Abhisek Ganguly
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductiv…
Randomness and signal propagation in physics-informed neural networks (PINNs): A neural PDE perspective
Jean-Michel Tucny, Abhisek Ganguly, Santosh Ansumali +1
Physics-informed neural networks (PINNs) often exhibit weight matrices that appear statistically random after training, yet their implications for signal propagation and stability…
A kinetic-based regularization method for data science applications
Abhisek Ganguly, Alessandro Gabbana, Vybhav Rao +2
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpol…